?url_ver=Z39.88-2004&rft_id=arXiv%3A1611.01265&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Feprints.imtlucca.it%2F3669%2F&rft.title=Dispersive+wave+propagation+in+two-dimensional+rigid+periodic+blocky+materials+with+elastic+interfaces&rft.creator=Bacigalupo%2C+Andrea&rft.creator=Gambarotta%2C+Luigi&rft.subject=T+Technology+(General)&rft.description=Dispersive+waves+in+two-dimensional+blocky+materials+with+periodic+microstructure+made+up+of+equal+rigid+units+having+polygonal+centro-symmetric+shape+with+mass+and+gyroscopic+inertia%2C+connected+each+other+through+homogeneous+linear+interfaces%2C+have+been+analysed.+The+acoustic+behavior+of+the+resulting+discrete+Lagrangian+model+has+been+obtained+through+a+Floquet-Bloch+approach.+From+the+resulting+eigenproblem+derived+by+the+Euler-Lagrange+equations+for+harmonic+wave+propagation%2C+two+acoustic+branches+and+an+optical+branch+are+obtained+in+the+frequency+spectrum.+A+micropolar+continuum+model+to+approximate+the+Lagrangian+model+has+been+derived+based+on+a+second-order+Taylor+expansion+of+the+generalized+macro-displacement+field.+The+constitutive+equations+of+the+equivalent+micropolar+continuum+have+been+obtained%2C+with+the+peculiarity+that+the+positive+definiteness+of+the+second-order+symmetric+tensor+associated+to+the+curvature+vector+is+not+guaranteed+and+depends+both+on+the+ratio+between+the+local+tangent+and+normal+stiffness+and+on+the+block+shape.+The+same+results+has+been+obtained+through+an+extended+Hamiltonian+derivation+of+the+equations+of+motion+for+the+equivalent+continuum+that+is+related+to+the+Hill-Mandel+macro+homogeneity+condition.+Moreover%2C+it+is+shown+that+the+hermitian+matrix+governing+the+eigenproblem+of+harmonic+wave+propagation+in+the+micropolar+model+is+exact+up+to+the+second+order+in+the+norm+of+the+wave+vector+with+respect+to+the+same+matrix+from+the+discrete+model.+To+appreciate+the+acoustic+behavior+of+some+relevant+blocky+materials+and+to+understand+the+reliability+and+the+validity+limits+of+the+micropolar+continuum+model%2C+some+blocky+patterns+have+been+analysed%3A+rhombic+and+hexagonal+assemblages+and+running+bond+masonry.&rft.publisher=arXiv&rft.date=2016&rft.type=Working+Paper&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.language=en&rft.rights=cc_by_nc&rft.identifier=http%3A%2F%2Feprints.imtlucca.it%2F3669%2F1%2F1611.01265.pdf&rft.identifier=++Bacigalupo%2C+Andrea+and+Gambarotta%2C+Luigi++Dispersive+wave+propagation+in+two-dimensional+rigid+periodic+blocky+materials+with+elastic+interfaces.++Working+Paper+++arXiv+++++++(Submitted)+++&rft.relation=https%3A%2F%2Farxiv.org%2Fabs%2F1611.01265&rft.relation=arXiv%3A1611.01265